Amplifying system



ii I

H. WHITTLE ET AL AllPLIFYiNG SYS'IBI Filed Nov. 13, 1925 FREQUENCY I'll-5+ v May 21,1929.

FREQUENCY hum/am.- Mace WJ/W/e M rd nivamer fl fiyJ' Patented May 21, 1929.

UNITED STATES PATENT OFFICE.

HORACE WHITTLE AND ARTHUR J. CHRISTOPHER,

OF NEW YORK, N. Y., ASSIGNORS TO WESTERN ELECTRIC COMPANY, INCORPORATED, OF NEW YORK, N. Y., A COB- I'ORATION OF NEW YORK.

AMPLIFYING SYSTEM.

Application filed November This invention relates to amplifying systems, and more particularly to networks used to couple two or more space discharge amplifiers in tandem.

An object of the invention is to secure a uniform voltage transformation of waves within a prescribed substantial range of frequencies.

Another object is to increase the over-all amplification of a space discharge amplifier to the maximum degree consistent with uniform amplification throughput a prescribed band of frequencies.

A further object is to provide a coupling circuit for multi-stage amplifiers in which are combined the properties of Voltage transformation and of broad-band frequency selectivity. A feature of the invention lies in the use of a pair of coupled tuned circuits to constitute a Wave transforming network and in the manner of proportioning the network coefficients to secure the desired objects.

The properties of a network comprising two coupled tuned circuits are well known in ageneral way, one of the most familiar characteristics being the double resonance oc cur-ring at frequencies separated by an interval which is determined by the coefficient of coupling. ,Transmission through a network of this type is characterized by large output currents or voltages at the two resonance fre caused the use of simple coupled circuits to be restricted to the selective transmission of very narrow wave bands, under which condition the two resonance frequencies are practically merged together.

By proportioning the coeificients of the coupling circuit in accordance with the present invention, it is found that all waves of frequencies within a substantially wide range, limited by the resonance frequencies, can be transformed in a substantially uniform degree, and transmitted with little loss of energy, while waves outside of these limits are strongly attenuated.

The nature of the invention and manner of its application will be'fully understood by referring to the following detailed descrip- 13, 1925. Serial No. 88,784.

indicated. The coupling circuit comprises an anti-resonant circuit 5 connected between points A and B in the anode circuit of amplifier l, and a second anti-resonant circuit 6 inductively coupled to circuit 5 and connected between terminals C and D in the input circuit of amplifier 2. Circuits 5 and 6 are proportioned to resonate at substantially the same resonance frequency. A non-inductive resistance 7 is also connected between terminals C and D to form a terminating impedance for the coupling circuit. This resistance may in certain cases be constituted, at least in part, by the space resistance between the grid and cathode of the succeeding amplifier. The co eflicients of. the capacity elements in antiresonant circuits 5 and 6 are denoted by C and 0 respectively, and the inductances by L and L Capacity 0 may be provided by a separate condenser, but in the preferred arrangement the tuned circuit 6 is so proportioned that resonance is effected with the self capacity of the inductance coil together with the inputcapacity of amplifier 2.

The relationships involved in proportioncies and to the voltage transformation ratio, but also to re uirements of transmission efii ciency, is exp ained in the following mathematical analysis.

For the pur ose of the analysis, the essential parts of Fig.' l are shown in a simplified schematic form in Fig. 2. In this schematic, the sending end impedance R corres onds to the space path resistance of ampli er 1, and the electromotive force E of the wave source is the repeated electromotive force corresponding to the wave impressed on the ampliher. The transformer formed by coupled inductances L and L is re laced by the well known equivalent T networ the inductances of the arms of which are designated in terms of the self inductances L and L and the mutual inductance M. Resistance R in Figure 2 corresponds to the terminating resistance 7. The only element of amplifier 2 that enters into the circuit is its input capacity, and Cthis is assumed to be included in capacy 2- A method of computing the output currents and voltages in a transmission circuit such as is shown in Fig. 2 is described fully by O. J Zobel, Transmission characteristics of electric wave filters, Bell System Technical J ournal, Volume III, No. 4, October 1924, page 567. In accordance with this method it is necessary first to determine certain parameters of the coupling circuit, known as the image parameters, which comprise image impedances corresponding to each pair of terlninals, and the image transfer or propagation constant. By means of these parameters and the terminating impedances of the system, the output currents and voltages may be 'computed, suitable formulae for this computation eing given by equations 69 and 70 in the article by Zobel mentioned above.

The advantages of this method lie in the comparative ease with which the ima e parameters of a network composed of su stantially pure reactances can be computed, and in the fact that the dominating characteristics of the system can be arrived at by a study of the image parameters alone. A property of the image parameters that is of great. help in making qualitative analysis of a circuit is this, that when the image impedance at either end is equal to the terminating impedance there is no reflection at that end, and, furthermore, the disparity of the two impedances is a measure of the amount of reflection that takes place.

The transfer constant is a measure of the ratio of the input and the output currents and voltages when the condition holds that the terminating impedances are respectively equal to the image impedances. Under this condition it is equal to the natural logarithm of the current or the voltage ratio corrected to correspond to unity transformation ratio in the network.

LetW andW denote the image impedances of the coupling circuit of Figs. 1 and 2 at the terminals AB and CD respectively, and let T be the image transfer constant of the circuit. Then, as explained in the reference above, W W and T may be computed from the open circuit impedances X and X}, of the coupling circuit, measured at terminals AB and CD respectively, and the corresponding short circuit impedances Y and Y These uantities are relatedby the following equations:

The computation of the open circuit and the short circuit impedances is a straight forward algebraic process, but ifan attem t is made to take into account the resistance 0 the reactive elements, the resulting expressions are likely to be very cumbrous. In the coupling circuit of this invention, as in practically all selective circuits, the reactive elements are so constructed as to.have a very small resistance in comparison with their reactances, and it is practicable to assume that the resistances are zero.

Assuming that the elements of the coupling circuit are pure reactances, and bearing in mind that the two anti-resonant circuits are resonant at the same frequency,.the following equations, by which the image impedances are expressed in terms of the wave fre uency and f may be derived with the help of quation 1: aga f "(2) fix)" 1 and and (4) At the limiting fre uencies W. is infinite and at frequencies outsi e of the limits the impedance is reactive. W bears a constant numerical ratio to W,,.

Between the limits 1, and f, the image impedances are resistive because of the fact that the open circuit and short circuit impedances are reactances of opposite sign and are therefore expressed by imaginary quantities of opposite sign the product of which is positive. It follows that the ratio of the two impedances is negative throughout this frequency range and hence that the transfer constant is imaginary. Conversely, the transfer constant is a real quantity at frequencies outside the range between frequencies f, and f The coupling network thus possesses characteristics similar to those of a broad band filter. Throughout a range of frequencies limited by f, and f,, the waves are not attenuated but are merely shifted in phase, while at other frequencies they are strongly attenuated. These characteristics are, however, modified to a greater or less extent by reflections 'at the terminals when the terminating impedances are not equal at all frequencies to the image impedances.

In the design of coupled tuned circuits it has not hitherto been the practice to take the terminal reflection losses into account, and in consequence it has not been possible to secure the uniform amplification ofaselected band of frequencies, except in cases where the selected band is very narrow in proportion to its mean frequency. In the coupling circuit of the invention the reflection effects are reduced to an unimportant amount by making the image impedances substantially'equal to the terminating impedances throughout the greater part of free transmission range.

Equations 2, 3 and 4 suffice to determine the design in accordance with the following procedure:

v The band of waves it is desired to transmit fixes the frequencies f, and f from which the common resonance frequency f and the coefficient of coupling k may be found by means of Equations 4. The next step is to determine the capacity C of the primary tuned circuit by means of Equation 2, the condition being specified that W is equal to the internal resistance R of amplifier 1 at some convenient frequency near the middle of the transmission range. The primary inductance L can be calculated from the value of C, and the frequency f The individual elements of the secondary circuit, L and C are thereafter determined with the help of Equation 3 which takes the transformation ratio into account. As an aid to performing the second design step, whereby the matchin of the impedances is secured, it is of value to know the general form of the frequency characteristic of the image impedance. The variation of W is shown in Fig. 3 in which curves a and a correspond to reactances, and curve 6 to resistive impedance. The resistive branch of the curves varies from an infinite value at each limiting frequency to a minimum value at an intermediate frequency which is generally close to f,. Perfect matching can not be obtained when the terminating impedance is a constant resistance but satisfactory matching is obtained when the circuit is de signed so that its minimum resistance is equal to the amplifier resistance R,. A much better result is obtained by making the mini mum value of the image impedance about 20% smaller than the amplifier resistance,

thereby securm .exact equality at two frequencies near e limiting fre uencies and reducing the disparity to a sma 1 amount at all frequencies except those very close to the limits.

The optimum value of the amplifier resistance in relation to the image impedance is indicated roughly by the horizontalline CO in Fig. 3.

he following exglicit formulae, giving the circuit element coe cients directly in terms of the limiting frequencies, may be developed from Equations 2, 3, and 4:

(1) coefficient of coupling (2) resonance frequency f 4 1 1 2 v o f1 fz (3) minimum value of W denoted by W (4) primary inductance frfr L ,n 1 -1. X f. (5) primary capacity (6) secondary inductance L L X R1 L] X 02 In the preferred form the capacity 0 is provided y the effective input capacity of amplifier 2 and the self capacity of coil L This capacity is likely to be slightly variable with frequency because the input capacity of the amplifier is dependent upon the value of the load impedance in the amplifier output circuit and to keep the variation a minimum it is necessary that the load impedance in the amplifier output circuit be fairly constant throughout the free transmission range. When anumber of amplifiers are connected .able transformation ratio.

dotted line represents the reactance com-- ponent and the continuous line the resistance component. The resemblance between Figs. 3 and 4 isnoticeable, this being due to the substantial elimination of reflection losses by the design proportions. The substantial uniformity of the impedance throughout the transmission band is also noticeable.

From Equation 3 it is seen that the impedance transformation ratio is 'equal to Q 0 I and hence that the voltage transformation ratio is equal to Since G, is fixed by the band width and the specified value of the input image impedance it follows that the minimum obtainable value of 0 determines the maximum obtain- Hence by constructing the secondary winding of the transformer so that it resonates at the proper'frequency when connected to the input terminals of the succeeding am lifier, the maximum ossible voltage trans ormation is obtained.

t is to be noted that the capacity C and hence the impedance transformation is inverse'ly proportional to the frequency band width, and also that it is independent of the location of the band in the wave spectrum.

The transmission characteristic of the coupling system is shown in Fig. 5, the curve representing the variation with respect to frequency of the gain or amplification, which is arbitrarily-defined in this case as the logarithm of the ratio of. the voltage between the output terminals CD to the volta e E generated in the space path of ampli er 1. This curve is typical of the uniformity that has been obtained in circuits constructed in accordance with the invention.

The invention finds application particularly in amplification systems designed to amplify selectively waves of a relatively wide range of frequencies. For example, in radio telephone receiving systems of the super heterodyne, or successive detection type it may be applied to the amplification of the intermediate frequency waves. In systems of this type the invention provides for uniform amplification of a band of waves usually about 10,000 to 15,000 cycles in width and located at a mean frequency in the neighborhood of 50,000 cycles, at the same time other frequencies are suppressed, and a substantial voltage transformation of four or five times can easily be obtained in each inter-stage circuit. Other applications of the invention may readily be perceived.

What is claimed is:

1. In combination with a pair of unequal terminal impedances, a coupling network comprising two electrically coupled antiresonant circuits tuned to the same frequency and connected respectively in shunt to said terminal impedances, the coupling of said circuits being proportioned to provide free transmission for waves of a, substantial band of frequencies between preassi ned limiting frequencies f, and f centered a out the common anti-resonance frequency, and the inductance L and capacity C'of each of said.

' circuits being'related in accordance with the formula L fo' f 2 ff 1 in which \V-is substantially equal to the associated terminal impedance, and 7, denotes the common anti-resonance frequency, whereby substantially uniform transmission is provided throughout the selected frequency range.

2. An am lifier system comprising two three-electro e space discharge amplifiers and a -frequency selective network adapted to connect said-amplifiers in tandem, said network comprising an anti-resonant circuit included in a circuit between the anode and the cathode of the first of the tandem connected amplifiers, and a second anti-resonant circuit included in a circuit between the control electrode and the cathode of the second amplifier, said. circuits being tuned to the same frequency and having a degree of coupling to provide free transmission for waves of a substantial band of frequencies, between preassigned limiting frequencies f, and f centered about the common anti-. resonance frequency, the inductance Ia and the capacity (J of the first of said circuits being related by the formula our names this 12th day of November, A. D. Y

1925. HORACE WHI'ITLE.

ARTHUR J. CHRISTOPHER. 

